Download Snímek 1 - Cesta k vědě - Gymnázium Jaroslava Seiferta

PTFE resonance
Banana
Introduction
Nuclear magnetic resonance (NMR) is a physical phenomenon based upon the quantum mechanical magnetic properties of an atom's nucleus.
All nuclei that contain odd numbers of protons or neutrons have an intrinsic magnetic moment and angular momentum. The most commonly measured nuclei are 1H (the most
receptive isotope at natural abundance) and 13C, although nuclei from isotopes of many other elements (in our measurement 19F) can also be observed.
NMR resonant frequencies for a particular substance are directly proportional to the strength of the applied magnetic field, in accordance with the equation for the Larmor precession
frequency. Because Larmor precession is typical, we can recognize what particles we are studying. And that is what NMR is about.
Theory
NMR apparatus
If a nucleus is placed in a magnetic field, the interaction between the nuclear magnetic moment
and the external magnetic field means the two states no longer have the same energy. The energy
of a magnetic moment μ when in a magnetic field B0 (the zero subscript is used to distinguish this
magnetic field from any other applied field) is given by the negative scalar product of the vectors:
E   Bo     z Bo
where the magnetic field has been oriented along the z axis.
It follows:
o
As a result the different nuclear spin states have different energies in a non-zero magnetic field. In
hand-waving terms, we can talk about the two spin states of a spin ½ as being aligned either with
or against the magnetic field. If γ is positive (true for most isotopes) then m = ½ is the lower energy
state.
E  mB
The energy difference between the two states is

 

 E 1    E 1   E  Bo
 I    I  
2 
2 


and this difference results in a small population bias toward the lower energy state.
We used a set of devices for NMR from Leybold instruments
inc. But we needed also some other devices:
• teslameter
• ampermeter
• stable power supply (the original one was fluctating)
• digital oscilloscope Tektronix DPO 4054 (we used digital
one because it allowed us to analyze the data in a
computer)
Resonance
Resonant absorption will occur when electromagnetic radiation of the correct frequency to match
this energy difference is applied. The energy of a photon is E = hf, where f is its frequency. Hence
absorption will occur when
E Bo
f 

h
2
These frequencies typically correspond to the radio frequency range of the electromagnetic
spectrum.
It is this resonant absorption that is detected in NMR.
Measurement and results
After we have understood the principles of NMR and made the apparatus work, we made 2 experiments. The first one (g factor measurement) was from the
instruction sheet. We thought up the second one, quantity of hydrogen in a sample.
G factor measurement
Quantity of hydrogen in a sample
G factor is a number typical for every nucleus. It is the proportion of
magnetic field and Larmor frequency in these the resonation of the sample
happens. We know the exact value of the frequency, because the oscillator
creates it. But the value of magnetic field is measured only indirectly from
the value of electric current in the coils.
The dependence of magnetic field on electric current cannot be easily
counted so we had to measure behavior of magnetic field as a function of
the electric current and then fit this to a function.
From this function we were then probing what magnetic field is applied on
the sample.
We measure resonance of the nuclei of the same element in the
same magnetic field and at the same temperature. The area of
the signal directly proportional to the quantity of the element in
the sample. This way we can discover quantity of an element in
the sample if we know the quantity of the same element in other
sample.
We knew quantity of hydrogen in the distilled water, so we were
able to measure the quantity of hydrogen in any other sample
that fits to the measuring tube.
600.0
Magnetic induction [T]
500.0
Resonance signal of
distilled water
400.0
S With
hysterezí
hysteresis
Sample
Results
Table results
Glycerin
(hydrogen)
5,76
5,59
PTFE (fluor)
5,44
5,25
300.0
bez
hystereze
Without
hysteresis
200.0
100.0
pokusné
bez někdy s
First, notměření
very exact
někdy
bez
hystereze
measuerement
To be able to count the area of the signal (red) we needed to fit it to a function
(green). Then we integrated it and we got these results:
0.0
0
1
2
3
4
5
6
Sample
Area
Quantity H [%]
Water
0,017516
11.11%
Banana
0,048454
30.73%
Apple
0,058327
37%
Electric current [A]
By measurement we had a little problem with hysteresis but we avoided it
later.
Then we measured electric current flow trought the sensing coil at selected
frequencies and calculated the g-factor from obtained current values.
We were surprised by the result because we thought that there is more hydrogen
in water then in banana or apple.
We think it is because there is much more hydrogen in long and complicated
carbohydrates.
www.gymjs.net
This experiment is a part of project Cesta k Vědě, that is supported by European Union and by
Prague municipal authority, it was made by two students from Gymnázium
Jaroslava Seiferta, Jan Kubant and Tomáš Přeučil. But we could not make it without help of our
tutors, Ing. David Tlustý and Ing. Michal Petráň.
www.gchd.cz
www.sladarna.cz
www.fjfi.cvut.cz, www.jaderka.cz
www.praha-mesto.cz
www.esfcr.cz